In his address to the people, Holness, the first prime minister to be born after Jamaica gained independence in 1962, paid tribute to the spirit of that time.
He noted it must have been a period of excitement as people witnessed the birth of a nation.
"Greatness within sight and within grasp it must have been a glorious time," he said.
Holness was elevated to the position of prime minister following endorsements from the outgoing prime minister Bruce Golding and government Members of Parliament.
He is expected to reveal his Cabinet soon.
Outgoing prime minister, Bruce Golding this afternoon tendered his resignation to Governor General Sir Patrick Allen, paving the way for Andrew Holness to become the head of government.
Golding noted the Andrew Holness administration will continue the reform programme and he expressed confidence in the ability of the incoming prime minister to effectively manage the country.
While addressing members of the private sector and diplomatic community on the weekend, Holness emphasised that he was also prepared to make tough decisions to drive the development the country needs at this time.
